Inside the Horizon with AdS/CFT

TL;DR

This paper explores how spacelike singularities and horizons in AdS/CFT can be described via analytically continued amplitudes, providing finite Lorentzian results and insights into black hole complementarity.

Contribution

It introduces a method to describe horizons and singularities in AdS/CFT using analytic continuation, connecting different bulk descriptions and addressing divergences.

Findings

Finite Lorentzian amplitudes are obtained through analytic continuation.

Two bulk descriptions correspond to different analytic continuations.

The approach supports the idea of black hole complementarity.

Abstract

Using the eternal BTZ black hole as a concrete example, we show how spacelike singularities and horizons can be described in terms of AdS/CFT amplitudes. Our approach is based on analytically continuing amplitudes defined in Euclidean signature. This procedure yields finite Lorentzian amplitudes. The naive divergences associated with the Milne type singularity of BTZ are regulated by an $i\epsilon$ prescription inherent in the analytic continuation and a cancellation between future and past singularities. The boundary description corresponds to a tensor product of two CFTs in an entangled state, as in previous work. We give two bulk descriptions corresponding to two different analytic continuations. In the first, only regions outside the horizon appear explicitly, and so amplitudes are manifestly finite. In the second, regions behind the horizon and on both sides of the singularity appear, thus yielding finite amplitudes for virtual particles propagating through the black hole singularity. This equivalence between descriptions only outside and both inside and outside the horizon is reminiscent of the ideas of black hole complementarity.